On steady compressible flows with compact vorticity; the compressible Hill's spherical vortex

A Vortex Particle Method for Compressible Flows

A vortex particle method for the simulation of twodimensional compressible flows is developed. The computational elements are Lagrangian particles that carry vorticity, dilatation, enthalpy, entropy and density. The velocity field is decomposed into irrotational and solenoidal parts, which allows its calculation in terms of the particles’ vorticity and dilatation. The particle coverage is trunc...

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows

Stability of Compressible Vortex Sheets in Steady Supersonic Euler Flows over Lipschitz Walls

We are concerned with the stability of compressible vortex sheets in two-dimensional steady supersonic Euler flows over Lipschitz walls under a BV boundary perturbation, since steady supersonic Euler flows are important in many physical situations. It is proved that steady compressible vortex sheets in supersonic flow are stable in structure globally, even under the BV perturbation of the Lipsc...

Vortex-like finite-energy asymptotic profiles for isentropic compressible flows

Bidimensional incompressible viscous flows with well-localised vorticity are well-known to develop vortex structures. The purpose of the present paper is to recover the asymptotic profiles describing these phenomena for homogeneous finite-energy flows as asymptotic profiles for near-equilibrium isentropic compressible flows. This task is performed by extending the sharp description of the asymp...

Modelling Compressible Multiphase Flows

We give in this paper a short review of some recent achievements within the framework of multiphase flow modeling. We focus first on a class of compressible two-phase flow models, detailing closure laws and their main properties. Next we briefly summarize some attempts to model two-phase flows in a porous region, and also a class of compressible three-phase flow models. Some of the main difficu...